In a series LCR circuit at resonance, the voltage across L is V L and across C is V C . These voltages are:

Equal in magnitude and same phase (add) according to standard textbooks

Zero in general practice as frequently described

Both equal to source voltage in most textbook accounts

In a series LCR circuit at resonance, the voltage across L is V…

Answer: Equal in magnitude and opposite in phase (cancel).

A Equal in magnitude and opposite in phase (cancel)
B Equal in magnitude and same phase (add) according to standard textbooks
C Zero in general practice as frequently described
D Both equal to source voltage in most textbook accounts

Correct answer: A. Equal in magnitude and opposite in phase (cancel)

Explanation: At resonance, V_L = IX_L and V_C = IX_C. Since X_L = X_C, |V_L| = |V_C|. But they are 180° out of phase with each other (V_L leads I by 90°, V_C lags I by 90°), so they cancel in series.

In a pure inductor the current lags the voltage by 90° (energy is briefly stored in the magnetic field before current responds); in a pure capacitor the current leads the voltage by 90° (current must flow to build up charge before voltage rises) - the mnemonic "ELI the ICE man" keeps these straight.

Concept context

AC circuits, impedance, LCR series circuit, resonance, transformers, and power factor.

Read the full Alternating Current notes →

In a series LCR circuit at resonance, the voltage across L is VL and across C is VC. These voltages are:

Concept context

More Alternating Current questions

In a series LCR circuit at resonance, the voltage across L is V_L and across C is V_C. These voltages are: